A comparison of three different stochastic population models with regard to persistence time

DOI10.1016/S0040-5809(03)00104-7zbMath1105.92023OpenAlexW2002882243WikidataQ35590069 ScholiaQ35590069MaRDI QIDQ851322

Linda J. S. Allen, Edward J. Allen

Publication date: 20 November 2006

Published in: Theoretical Population Biology (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/s0040-5809(03)00104-7

zbMATH Keywords

Markov chainStochastic differential equationLogistic equationBackward Kolmogorov differential equationBirth and death processPersistence time

Mathematics Subject Classification ID

Applications of branching processes (60J85) Population dynamics (general) (92D25) Applications of Markov chains and discrete-time Markov processes on general state spaces (social mobility, learning theory, industrial processes, etc.) (60J20)

Related Items

Mathematical models for hantavirus infection in rodents ⋮ Rumor spreading model with noise interference in complex social networks ⋮ The role of stochasticity in noise-induced tipping point cascades: a master equation approach ⋮ A penalized simulated maximum likelihood approach in parameter estimation for stochastic differential equations ⋮ Establishing a beachhead: a stochastic population model with an Allee effect applied to species invasion ⋮ Environmental variability and mean-reverting processes ⋮ A Bayesian SIRS model for the analysis of respiratory syncytial virus in the region of Valencia, Spain ⋮ Threshold dynamics of a stochastic SIS epidemic model with nonlinear incidence rate ⋮ A hybrid epidemic model to explore stochasticity in COVID-19 dynamics ⋮ Extinction and persistence of a stochastic SIRV epidemic model with nonlinear incidence rate ⋮ The stochastic SEIR model before extinction: computational approaches ⋮ Optimal harvesting strategy based on uncertain logistic population model ⋮ Derivation and experimental comparison of cell-division probability densities ⋮ Uncertainty in clinical data and stochastic model for in vitro fertilization ⋮ Asymptotic dynamics of a stochastic SIR epidemic system affected by mixed nonlinear incidence rates ⋮ A stochastic model of fowl pox disease: estimating the probability of disease outbreak ⋮ Dynamics of Kolmogorov systems of competitive type under the telegraph noise ⋮ Optimal management of stochastic invasion in a metapopulation with Allee effects ⋮ Extinction-time for stochastic population models ⋮ On real-valued SDE and nonnegative-valued SDE population models with demographic variability ⋮ Parameter inference and model selection in deterministic and stochastic dynamical models via approximate Bayesian computation: modeling a wildlife epidemic ⋮ Existence and persistence of positive solution for a stochastic turbidostat model ⋮ Modeling nosocomial transmission of rotavirus in pediatric wards ⋮ An extended stochastic Allee model with harvesting and the risk of extinction of the herring population ⋮ A stochastic SIRS epidemic model with infectious force under intervention strategies ⋮ Demographic stochasticity in the SDE SIS epidemic model ⋮ Persistence-time estimation for some stochastic SIS epidemic models ⋮ Continuum Approximation of Invasion Probabilities ⋮ A mean extinction-time estimate for a stochastic Lotka-Volterra predator-prey model ⋮ A stochastic epidemic model for the dynamics of two pathogens in a single tick population ⋮ Derivation of stochastic partial differential equations for size- and age-structured populations ⋮ Comparison of Markov Chain and Stochastic Differential Equation Population Models Under Higher-Order Moment Closure Approximations ⋮ Construction of Equivalent Stochastic Differential Equation Models ⋮ Modelling algal densities in harmful algal blooms (HAB) with stochastic dynamics ⋮ A comparison of persistence-time estimation for discrete and continuous stochastic population models that include demographic and environmental variability ⋮ A martingale formulation for stochastic compartmental susceptible-infected-recovered (SIR) models to analyze finite size effects in COVID-19 case studies ⋮ Mathematical analysis of a hybrid model: impacts of individual behaviors on the spreading of an epidemic ⋮ Doubling-Time Probability Densities For Growth Processes ⋮ Hopf bifurcation of the stochastic model on HAB nonlinear stochastic dynamics

Cites Work

• Stability analysis of a stochastic logistic model
• Moment closure and the stochastic logistic model
• How to avoid extinction of populations optimally exploited
• Logistic population growth under random dispersal
• Persistence in density dependent stochastic populations
• Higher-order implicit strong numerical schemes for stochastic differential equations
• Numerical solution of SDE through computer experiments. Including floppy disk
• Carrying capacity and demographic stochasticity: Scaling behavior of the stochastic logistic model.
• Stochastic population models. A compartmental perspective
• Effects of immigration on some stochastic logistic models: A cumulant truncation analysis
• Simple stochastic models and their power-law type behaviour.
• Metastability, a consequence of stochastics in multiple stable population dynamics
• Extinction of populations by random influences
• On the extinction of a colonizing species
• On the distribution of the time to extinction in the stochastic logistic population model
• Modelling Biological Populations in Space and Time
• Numerical Solution of First Passage Problems in Random Vibrations
• Handbook of stochastic methods for physics, chemistry and natural sciences.
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item